Stability Of Frequency Standards Research Articles

Palm-sized, vibration-insensitive, and vacuum-free all-fiber-photonic module for 10−14-level stabilization of CW lasers and frequency combs

Compact and robust frequency-stabilized laser sources are critical for a variety of fields that require stable frequency standards, including field spectroscopy, radio astronomy, microwave generation, and geophysical monitoring. In this work, we applied a simple and compact fiber ring-resonator configuration that can stabilize both a continuous-wave laser and a self-referenced optical frequency comb to a vibration-insensitive optical fiber delay-line. We could achieve a thermal-noise-limited frequency noise level in the 10 Hz–1 kHz offset frequency range for both the continuous-wave laser and the optical frequency comb with the minimal frequency instability of 2.7 × 10−14 at 0.03-s and 2.6 × 10−14 at 0.01-s averaging time, respectively, under non-vacuum conditions. The optical fiber spool, working as a delay reference, is designed to be insensitive to external vibrations, with a vibration sensitivity of sub-10−10 (1/g) and a volume of 32 ml. Finally, the ring-resonator setup is packaged in a palm-sized aluminum case with 171-ml volume with a vibration-insensitive spool, as well as an even smaller 97-ml-volume case with an ultracompact 9-ml miniaturized fiber spool.

Proposal for a hybrid clock system consisting of passive and active optical clocks and a fully stabilized microcomb.

Optical atomic clocks produce highly stable frequency standards and frequency combs bridge clock frequencies with hundreds of terahertz difference. In this paper, we propose a hybrid clock scheme, where a light source pumps an active optical clock through a microresonator-based nonlinear third harmonic process, serves as a passive optical clock via indirectly locking its frequency to an atomic transition, and drives a chip-scale microcomb whose mode spacing is stabilized using the active optical clock. The operation of the whole hybrid system is investigated through simulation analysis. The numerical results show: (i) The short-term frequency stability of the passive optical clock follows an Allan deviation of σy(τ) = 9.3 × 10-14τ-1/2 with the averaging time τ, limited by the population fluctuations of interrogated atoms. (ii) The frequency stability of the active optical clock reaches σy(τ) = 6.2 × 10-15τ-1/2, which is close to the quantum noise limit. (iii) The mode spacing of the stabilized microcomb has a shot-noise-limited Allan deviation of σy(τ) = 1.9 × 10-11τ-1/2. Our hybrid scheme may be realized using recently developed technologies in (micro)photonics and atomic physics, paving the way towards on-chip optical frequency comparison, synthesis, and synchronization.

Research on generation of stable mid-infrared lasers with narrow linewidths based on optical feedback locking

Mid-infrared precision spectroscopy has important applications in the fields of trace gas detection and the determination of fundamental physical constants. However, due to the limited commercialization of related technologies, there is a lack of narrow linewidth laser sources or linewidth narrowing approaches in the mid-infrared region, as well as stable mid-infrared frequency standards. The most commercialized and widely used mid-infrared laser source is the quantum cascade laser (QCL). But its free-running linewidth is more than MHz scale due to the influence of laser drive current noise and temperature fluctuation. This impedes the development of precision spectroscopy in this region. In this work, we introduce a technique for generating a narrow linewidth, stable mid-infrared laser by using optical feedback frequency locking, with a high-finesse mid-infrared ultrastable Fabry-Pérot cavity as the frequency reference. The optical cavity consists of two high reflectivity mirrors separated by ultra-low expansion (ULE) material with a low temperature expansion coefficient, and its temperature is precisely controlled. And the cavity is also surrounded in a vaccum cavity made of stainless steel. All these measures ensure the cavity length and its longitudinal mode stability. By using optical feecback, a QCL is locked to the cavity, which stabilizes the laser frequency and narrows the laser linewidth. In order to improve the long-term stability of the optical feedback, an active servo is leveraged to control the feedback phase. The error signal for the servo is obtained by using the method similar to the Pound-Derver-Hall locking. In this work, we first theoretically analyze the feasibility of laser to F-P cavity frequency locking by optical feedback. We propose the laser frequency response model with a linear F-P cavity under optical feedback, and analyze the influence of the direct cavity reflection on the laser frequency. Then the experimental demonstration is conducted. Firstly, we measure the reflectivity of the cavity mirror by using cavity ring-down spectroscopy, resulting in a cavity finesse of 30200 and a cavity mode linewidth of 49.7 kHz. After that, we successfully achieve optical feedback frequency locking, and consecutive cavity transmission is observed. The error signal for the control of the optical feedback phase is used to evaluate the locking performance by converting it into the laser frequency noise. By analyzing the noise spectral density, the QCL linewidth is narrowed to 0.3 Hz on a short timescale (< 10 ms). And the long-term stability is suspected to be dedicated by the temperature variation of the optical cavity, resulting in a laser frequency drift 20 kHz/12 h. The narrow linewidth stabilized mid-infrared laser source obtained with this technique is expected to serve as an effective frequency reference source for mid-infrared precision spectroscopic measurements.

Relativistic gravimetry

Work on the creation of a device that will be able to measure the parameters of the Earth’s gravitational field in space was started at the State Design Office «Yuzhnoye» in 2001 as part of the formation of a scientific research program on the «Sich-1M» spacecraft. But since there were no devices in the world to directly measure the parameters of the Earth’s gravitational field in space, the idea arose to use the relativistic «red shift» effect to solve this problem. The possibility of practical implementation of this idea arose in 2008—2010 during the implementation of the STCU project No. 3856 «Measurement of the parameters of the Earth’s gravitational field using navigation satellite systems». Within the framework of this project, for the first time, a differential radiophysical gravimeter was created and tested, in which the radiation of navigation satellites was used as a source of highly stable radiation. Radiophysical method for measuring the parameters of the Earth’s gravitational field based on the results of dissertation research, 4 patents for an invention of Ukraine, 2 copyright certificates were obtained, and 16 articles were published in scientific journals. In 2012, the fundamental patent No. 98358 «Method for measuring geodetic parameters and a device for its implementation» was obtained, which was recognized in 2014 as the best patent of Ukraine in the absolute nomination in the competition «Best Patent of Ukraine». This patent formed the basis for the creation of the «Gravika» — navigation control and correction station. This work has been continued at JSC «RPC «KURS» since 2015. Since 2015, JSC «RPC «KURS» has been the head organization in the NSAU for the creation of a coordinate-clock and navigation support network for Ukraine. In 2016, it was created, certified and put into operation control and correction station (CCS) «Gravika», which can simultaneously operate both as a navigational base station and as a gravimeter, that is, to solve a complete geodetic problem. The principle of operation of the gravimeter is based on the relativistic effect of «red shift». One of the main technical and economic problems is the need to use a highly stable hydrogen frequency standard as part of the Gravika control and correction station, the cost of which is at least USD 80,000 (code «Geomonitoring») in order to develop a concept for creating, on the basis of the existing network of coordinate-clock and navigation support in Ukraine, a complex a clear geophysical monitoring system using the Gravika control and correction station and a satellite system for relaying signals of a highly stable TWSTFT frequency standard. Such a solution will make it possible to abandon the use of a frequency standard at each station and thereby reduce the cost of the CCS and the system as a whole. In addition, the work of the CCS «Gravika» showed the possibility of predicting seismic activity within a radius of 500 km from the station. A three-axis version of the gravimeter was also implemented, which allows you to simultaneously measure the absolute, relative values of the gravitational acceleration and the angle of inclination of the gravitational acceleration vector. Such functionality makes the radiophysical gravimeter indispensable when used on mobile vehicles, including space vehicles.

Time: Astronomical time - atomic time - redefining second based on constant

The evolution history of modern time from the astronomical time to the atomic second is briefly reviewed herein. The progress and status of realizing the current definition of the second using cesium cold atomic fountain primary frequency standards, the process of generating the international atomic time (TAI) and coordinated universal time (UTC), and trend of releasing the tolerance on inserting leap-seconds into the UTC are sketched. The present situation on steering the TAI regularly from January 2016 by cesium fountain frequency standards from five countries is reported. Research progress of local and global optical frequency standards is summarized, and steering TAI by six optical frequency standards starting from 2016 is reported. Requirements and responses on steering TAI regularly by optical frequency standards are introduced according to the roadmap, which is under discussion internationally, or the future redefinition of the second. Furthermore, two types of optical frequency standards, namely the basic-research and the metrological type are suggested, and the performance and technical qualifications for the metrological type of optical frequency standards are recommended. For the optical frequency standards of the metrological type, with uncertainties better than 3×10−17, not only static relative gravity but also the alternative tide frequency shifts should be considered in their frequency evaluations. Finally, a scheme employing frequency comparison, across a long longitude-distance, between two highly stable optical frequency standards to demonstrate the relativistic tidal frequency shift directly and experimentally is proposed.

Flexible Hybrid Approach for a 3D Integrated Physics Package of Chip-Scale Atomic Clocks

To realize the chip-scale atomic clocks (CSACs) for atomic reference with miniaturization and low power consumption, there are technological challenges in the physics package for compact and stable frequency standards. Here, the precise thermal management and the exact magnetic-field control of the physics package are required for accurate clocks. Also, high thermal resistance for the physics package helps to considerably reduce power consumption of the CSAC. Thus, in this study, a compact physics package with embedded magnetic shielding has been developed by using flexible hybrid approach for a chip-scale atomic clock. The vertical-cavity surface-emitting laser (VCSEL) and the MEMS hotplate on a flexible circuit board (FPCB) are vertically stacked and bound with a QWP and a MEMS vapor cell by aluminum foil. The aluminum bound structure is suspended by the polyimide core of the FPCB for high thermal resistance. Also, the mu-metal fixture is applied for magnetic shield and FPCB suspension, while the MEMS hotplate with a resistance heater and an amorphous Si based thermistor is adopted for thermal management of the physics package. Then, the planar integrated FPCB is folded and stacked vertically at an intersection with the mu-metal fixture. As a result, the CSAC incorporating the proposed physics package reveals the CPT linewidth of 5.6 kHz and low power consumption of about 200mW. The measured frequency short-term stability is about $5.2\times 10^{-12} \tau ^{-1/2}$ at 1000-second integration. The observed results demonstrate promising performances of the flexible hybrid physics package for its use in miniaturized atomic clocks.

Allan Variance Computed in Space Domain: Definition and Application to InSAR Data to Characterize Noise and Geophysical Signal.

The Allan variance was introduced 50 years ago for analyzing the stability of frequency standards. In addition to its metrological interest, it may be also considered as an estimator of the large trends of the power spectral density (PSD) of frequency deviation. For instance, the Allan variance is able to discriminate different types of noise characterized by different power laws in the PSD. The Allan variance was also used in other fields than time and frequency metrology: for more than 20 years, it has been used in accelerometry, geophysics, geodesy, astrophysics, and even finances. However, it seems that up to now, it has been exclusively applied for time series analysis. We propose here to use the Allan variance on spatial data. Interferometric synthetic aperture radar (InSAR) is used in geophysics to image ground displacements in space [over the synthetic aperture radar (SAR) image spatial coverage] and in time thanks to the regular SAR image acquisitions by dedicated satellites. The main limitation of the technique is the atmospheric disturbances that affect the radar signal while traveling from the sensor to the ground and back. In this paper, we propose to use the Allan variance for analyzing spatial data from InSAR measurements. The Allan variance was computed in XY mode as well as in radial mode for detecting different types of behavior for different space-scales, in the same way as the different types of noise versus the integration time in the classical time and frequency application. We found that radial Allan variance is the more appropriate way to have an estimator insensitive to the spatial axis and we applied it on SAR data acquired over eastern Turkey for the period 2003-2011. Spatial Allan variance allowed us to well characterize noise features, classically found in InSAR such as phase decorrelation producing white noise or atmospheric delays, behaving like a random walk signal. We finally applied the spatial Allan variance to an InSAR time series to detect when the geophysical signal, here the ground motion, emerges from the noise.

Application of Three-Cornered Hats for Frequency Stability Analysis of Atomic Clock

Three-Cornered Hats is a classical method to obtain the frequency stability of one single atomic clock without more stable frequency standards available. In this paper, the measurement data of three hydrogen masers in a ground station is used to analyze the frequency stability of one single atomic clock. The analysis steps and problems in application of this method are introduced. The negative values of the calculated Allan variance of one clock with averaging time larger than 4000s occur. It probably implies that the hypothesis of uncorrelated clocks is not acceptable, which will be analyzed further.

Allan deviation analysis of financial return series

We perform a scaling analysis for the return series of different financial assets applying the Allan deviation (ADEV), which is used in the time and frequency metrology to characterize quantitatively the stability of frequency standards since it has demonstrated to be a robust quantity to analyze fluctuations of non-stationary time series for different observation intervals. The data used are opening price daily series for assets from different markets during a time span of around ten years. We found that the ADEV results for the return series at short scales resemble those expected for an uncorrelated series, consistent with the efficient market hypothesis. On the other hand, the ADEV results for absolute return series for short scales (first one or two decades) decrease following approximately a scaling relation up to a point that is different for almost each asset, after which the ADEV deviates from scaling, which suggests that the presence of clustering, long-range dependence and non-stationarity signatures in the series drive the results for large observation intervals.

Study of astronomical and geodetic series using the Allan variance

Allan variance (AVAR) was first introduced more than 40 years ago as a estimator of the stability of frequency standards, and now it is actively used for investigations of time series in astronomy, geodesy and geodynamics. This method allows one to effectively explore the noise characteristics for various data, such as variations of station and source coordinates, etc. Moreover, this technique can be used to investigate the spectral and fractal structure of the noise in measured data. To process unevenly weighted and multidimensional data, which are usual for many astronomy and geodesy applications, AVAR modifications are proposed by the author. In this paper, a brief overview is given of using of classical and modified AVAR method in astronomy and geodynamics.

Precision Clock and Time Transfer on a Wireless Telecommunication Link

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Precise time dissemination is a key requirement for remote clock synchronization used in coordinated command of distributed actuators in various applications. We present a newly conceived low-cost clock system based on the time-to-digital converter (TDC) principle to generate, transfer, and compare time-coded sequences (TCSs) with nanosecond accuracy using a wireless telecommunication link. The clock principle counts pulse sequences with nanosecond precision derived from a low-frequency oven-controlled crystal oscillator (OCXO) stable frequency standard. The TCSs are transmitted to a remote transponder that distributes them to receiving stations, where the clock readings are processed. A simple short-range wireless telecommunication link was assembled to demonstrate the system. The repeated TCSs are received back and compared with the reference clock. We describe the clock, the telecommunication setup, and the electrical and electronic sources of delays. Comparison of mean TCSs taken every 0.629 s provided a time-domain midterm stability Allan deviation of about <formula formulatype="inline"><tex Notation="TeX">$1.3 \times 10^{-11}$</tex></formula> at <formula formulatype="inline"><tex Notation="TeX">$\tau = 10^{3}\ \hbox{s}$</tex></formula>. These results show the feasibility of a low-cost GPS-independent technique, exhibiting highly performing time-domain midterm stability. This system is a key requirement for a new proposed system for geopositioning. </para>

Formation of Ramsey fringes based on pulsed coherent light storage

We propose a new scheme of microwave frequency standards based on pulsed coherent optical information storage. Unlike the usual frequency reference where the Ramsey fringe is printed on the population of a certain state, we print the Ramsey fringe on the coherence. Then the coherence is detected in the form of a retrieval light. The central line of the Ramsey fringe can be used as a frequency reference in an absorption-cell-based atomic frequency standard. This scheme is free of light shifts as the interrogating process is separated from the optical pumping processes, and the cavity pulling effect is negligible due to the low Q requirement. Encoding the Ramsey interference into the retrieval light pulse has the merit of high signal to noise ratio and the estimated frequency stability of shot noise limit is about $2\times10^{-14}$ in 1 second, this scheme is promising for building small, compact and stable atomic frequency standards.

Possibility of using low-energy nuclear transitions as benchmarks for frequency stabilization

The fundamental possibility of using low-energy nuclear transitions for obtaining highly stable frequency standards is considered.

Millisecond and binary pulsars as nature's frequency standards -- II. The effects of low-frequency timing noise on residuals and measured parameters

Pulsars are the most stable natural frequency standards. They can be applied to a number of principal problems of modern astronomy and time-keeping metrology. The full exploration of pulsar properties requires obtaining unbiased estimates of the spin and orbital parameters. These estimates depend essentially on the random noise component being revealed in the residuals of time of arrivals (TOA). In the present paper, the influence of low-frequency ("red") timing noise with spectral indices from 1 to 6 on TOA residuals, variances, and covariances of estimates of measured parameters of single and binary pulsars are studied. In order to determine their functional dependence on time, an analytic technique of processing of observational data in time domain is developed which takes into account both stationary and non-stationary components of noise. Our analysis includes a simplified timing model of a binary pulsar in a circular orbit and procedure of estimation of pulsar parameters and residuals under the influence of red noise. We reconfirm that uncorrelated white noise of errors of measurements of TOA brings on gradually decreasing residuals, variances and covariances of all parameters. On the other hand, we show that any red noise causes the residuals, variances, and covariances of certain parameters to increase with time. Hence, the low frequency noise corrupts our observations and reduces experimental possibilities for better tests of General Relativity Theory. We also treat in detail the influence of a polynomial drift of noise on the residuals and fitting parameters. Results of the analitic analysis are used for discussion of a statistic describing stabilities of kinematic and dynamic pulsar time scales.

Laser-pumped and laser-cooled atomic clocks for space applications

Highly stable atomic frequency standards are of increasing importance for a variety of space applications, ranging from communication to navigation and time transfer to tests of fundamental science. We present a discussion of the improvements possible with laser pumping of vapor cell clocks, including applying coherent population trapping (CPT) techniques. We also present our progress toward a cold atom clock based on magneto-optically trapped atoms for space applications.

Effect of aperture averaging upon tropospheric phase fluctuations seen with a radio antenna

The spectrum of tropospheric phase fluctuations expected for a radio antenna at timescales &lt;100 s on a space to ground link has been calculated. A new feature included in these calculations is the effect of aperture averaging, which causes a reduction in delay fluctuations on timescales less than the antenna wind speed crossing time, ∼D/(8 m/s) (D is the antenna diameter). On timescales less than a few seconds, the Allan deviation σy(Δt) ∝ (Δt)+1, rather than σy(Δt) ∝ (Δt)−1/6 without aperture averaging. Calibration of tropospheric phase fluctuations with water vapor radiometers will not be possible on timescales less than ∼10 s, due to thermal radiometer noise. However, the tropospheric fluctuation level will be small enough that phase measurements on timescales less than a few seconds will be limited by the stability of frequency standards and/or other nontropospheric effects.

Ultra stable clocks for use in space

A number of experiments in the field of gravitation and relativity have been proposed that require highly stable frequency standards to be operated in space for extended periods. Clocks for such applications must have high frequency stability, small size and weight, low power comsumption, and high reliability. We discuss the characteristics of atomic clocks that are currently available for use in space and that may be available over roughly the next decade.

Very Long Baseline Interferometry in the Southern Hemisphere

Phase coherent interferometers with intercontinental baselines became possible because of the development of stable frequency standards. With sufficiently stable frequency standards, no connection is necessary between the two ends of an interferometer. The first VLBI experiments were conducted by a group at the University of Florida who used an intensity interferometer with independent tape recorders for observations of Jupiter. Later, they changed to a coherent system using crystal-controlled oscillators. Since then, several interferometer systems have been developed. A Canadian group developed a system using video tape recorders at each end of the interferometer. They recorded the data in analogue form and managed to bring the two tapes together and to synchronize them to an accuracy of better than a microsecond. After synchronization, the outputs were combined and fringes extracted. Their system has a bandwidth of about 4 MHz. No-one else has attempted a wide-band analogue system.

Progress and feasibility for a unified standard for frequency, time, and length

The recent successful extension of frequency synthesis upward in the infrared to the 88-THz frequency of the very stable methane frequency standard has implications for expanded uses of frequency/time metrology and hence of frequency/time dissemination systems. After further refinements of the infrared frequency synthesis techniques, metrologists will have the opportunity to define a value for the speed of light and to use a particular frequency standard --the most accurate one--as a unified standard for frequency, time, and length.

Short-term stability of passive atomic frequency standards

The instability of passive atomic frequency standards caused by shot noise introduced by the atomic reference is calculated. This instability can be characterized by a figure of merit for the atomic reference, and the asymptotic functions for the rms frequency fluctuation for long and short averaging times expressed in terms of this quantity. Measurements of the rms frequency fluctuation of cesium atomic beam and rubidium vapor frequency standards are compared with theory, and the predicted performances of various existing and proposed atomic standards are tabulated. It is feasible to build atomic beam frequency standards whose stability for averaging times less than one second is limited by noise in the crystal oscillator rather than by shot noise, a criterion generally met by rubidium vapor frequency standards. For long averaging times, shot noise will always be the fundamental limiting factor in atomic frequency standard stability.